This is Equation 7 in
the proof on pages 3 and 4 of the supplement to [1]}. From this point the proof goes through without change: the assumed and derived properties of \(g\)  require \(g(x)=k x\log x + (g^{\prime }(1)-k)(x-1)\)  and the second term doesn't contribute to \(D_g\)  as it integrates to zero.
